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Article
Explanation of Photon Navigation in the
Mach-Zehnder Interferometer
Dirk J. Pons
Department of Mechanical Engineering, University of Canterbury, Private Bag 4800,
Christchurch 8020, New Zealand; dirk.pons@canterbury.ac.nz
Received: 29 July 2020; Accepted: 26 September 2020; Published: 28 September 2020
Abstract: Photons in interferometers manifest the functional ability to simultaneously navigate both
paths through the device, but eventually appear at only one outlet. How this relates to the physical
behaviour of the particle is still ambiguous, even though mathematical representation of the problem is
adequate. This paper applies a non-local hidden-variable (NLHV) solution, in the form of the Cordus
theory, to explain photon path dilemmas in the Mach–Zehnder (MZ) interferometer. The findings
suggest that the partial mirrors direct the two reactive ends of the Cordus photon structures to different
legs of the apparatus, depending on the energisation state of the photon. Explanations are provided
for a single photon in the interferometer in the default, open-path, and sample modes. The apparent
intelligence in the system is not because the photon knows which path to take, but rather because
the MZ interferometer is a finely-tuned photon-sorting device that auto-corrects for randomness
in the frequency phase to direct the photon to a specific detector. The principles also explain other
tunnelling phenomena involving barriers. Thus, navigation dilemmas in the MZ interferometer may
be explained in terms of physical realism after all.
Keywords: photon locality; interferometer
1. Introduction
Particles show attributes of wave-particle duality behaviour in interferometer devices.
The behaviour manifests as a functional ability of the photon to simultaneously navigate both
paths through the device, but eventually appear at only one outlet. This behaviour may be functionally
represented in quantum formulations, but how this relates to the physical behaviour of the particle
is still ambiguous. Indeed, the level of residual ambiguity depends on the perspective taken,
and more mathematical worldviews may not perceive that there is anything left unexplained.
Nonetheless, from the perspective of classical physics, and also the philosophical position of physical
realism, there are conceptual difficulties reconciling the path navigation behaviour with notions of
particle composition. By this we do not mean that there is any lack of mathematical representation of
the problem, but rather that there is value in seeking ontologically richer perspectives grounded in
physical realism.
This paper extends previous work by applying a non-local hidden-variable (NLHV) solution,
in the form of the Cordus theory [1], to explain photon path dilemmas. The application is primarily to
the Mach–Zehnder interferometer, although the principles generalise to explain tunnelling.
2. Existing Approaches
Wave theory explains the situation as the interference of two waves. However, that only applies
to beams of light, whereas the empirical reality is that the behaviour also exists for individual photons.
Classical wave theory cannot explain this. Quantum mechanics (QM) began with the idea of light
being made of corpuscles, hence photons. Subsequent developments of quantum field theory (QFT)
Optics 2020, 1, 243–254; doi:10.3390/opt1030018 www.mdpi.com/journal/optics
Optics 2020, 1 244
provided a mathematical representation of the photon as a set of quantum oscillators, as opposed to a
particle with a specific position [2]. The operation of an interferometer, a likewise double-slit device,
is readily accommodated by QFT, even for a single photon. The photon is represented as having
two modes, which correspond to the two legs of the interferometer. Dirac [3] similarly noted that
“each photon [goes] partly into each of the two components” (p9). Thus, from the QFT perspective,
the photon is not simply a point particle, and is more than an electromagnetic plane wave and
wave packet. So, from within QFT, the navigation of the photon through the simple interferometer
does not present any difficulty. Nonetheless, QFT is not a complete theory (gravitation is excluded),
and the interferometer behaviour does present a conundrum when viewed more generally. Specifically,
there are ontological problems about the nature of photon identity from a realist perspective. Physical
realism is the assumption, based on experience in the everyday world, that observed phenomena
have underlying physical mechanisms [4]. From this perspective both classical and quantum physics
are incomplete descriptions of photon path behaviour, despite having acknowledged strengths in
other respects.
Other explanations for the path dilemma in wave-particle duality are intelligent photons and
parallel universes, but both have difficulties. The first assumes some intelligence in the photon: that
photons know when a path is blocked, without even going down it (e.g., Mach–Zehnder interferometer),
and adapt their behaviour in response to the presence of an observer (e.g., Schrodinger’s Cat, Zeno effect).
This also raises philosophical problems with choice and the power of the observer to affect the physical
world and its future merely by looking at it (contextual measurement). Thus, the action of observation
would affect the locus taken by a photon, and therefore the outcome. This concept is sometimes
generalised to the universe as a whole. The second explanation is the metaphysical idea of parallel
universes or many worlds, i.e., that each statistical outcome that does not occur in this universe does in
another [5]. From the perspective of physical realism, it is problematic that these other universes are
unobservable. It also means that the theory cannot be verified. Nor is it clear what keeps track of the
information content of the vast number of universes that such a system would generate. Both these
explanations are convenient ways of comprehending the practicalities of wave-particle duality, but they
sidestep the real issues.
Finally, there is the hidden variable sector of physics. This is based on the assumption that
particles have internal sub-structures that provide the mechanisms for the observed behaviours.
Although this principle is consistent with the expectations of physical realism, the sector as a whole
has been unproductive at developing useful theories. There was a historical attempt to explain path
dilemmas assuming hidden-variables in the form of the de Broglie-Bohm theory of the pilot wave [6,7].
However, it is debatable whether this really solves the problem. Nor has the concept progressed to
form a broader theory of physics that could explain other phenomena.
The above treatment of the quantum perspective of photons is brief and is not intended
to encompass the “true nature” of the photon (if that is even possible). Hence, the question of
non-localisation of photons [8,9], or whether an effective mass emerges for massless particles generally
when they interact [10], is skipped over here. By this we do not mean that there is any lack of value in
considering the problem from the localisation perspective, or any lack of mathematical representation
of the problem via quantum field theory, but rather that there is value in the ontologically different
perspectives that can be provided by other theories such as NLHV theory. A NLHV theory automatically
assumes non-locality occurs, and, hence, implicitly expects the photon to exist in more than one
location. Furthermore, the specific NLHV theory explored here has a field component with multiple
oscillators [11] and, hence, has elements that are not dissimilar to QFT. While NLHV theories may be
lacking in mathematical formalism, they do provide new insights. The various existing theories of
physics have historically benefited from findings from each other.Optics 2020, 1 245
3. Approach
The purpose of this work was to apply the Cordus theory to the photon path problem in
interferometers. This is a type of non-local hidden-variable (NLHV) theory, and, therefore, has an
explicit link between the functional attributes of the particle and a proposed inner causality. For the
origin ofOptics
this2020,
NLHV1, FOR concept
PEER REVIEW and its application to the double-slit device, see [1]. The theory 3 also
provides a derivation of optical laws (reflection, refraction, and Brewster’s angle) [1] and a description
origin of of
of the processes thisphoton
NLHV emission
concept andand itsabsorption
application to the double-slit
[12,13], conversiondevice, see [1]. The
of photons theory also
to electron-positron
provides a derivation of optical laws (reflection, refraction, and Brewster’s angle) [1] and a
in pair production [14], annihilation of matter-antimatter back to photons [15], the asymmetrical
description of the processes of photon emission and absorption [12,13], conversion of photons to
genesis production
electron-positronsequence
in pairfrom photons
production [14],to a matter universe
annihilation [16], and back
of matter-antimatter the origin of the
to photons finite
[15], the speed
of light [17].
asymmetrical genesis production sequence from photons to a matter universe [16], and the origin of
Thethe
approach
finite speedtaken was[17].
of light a conceptual one, using abductive reasoning. Design principles were used
The approach taken
to logically infer the requisite internalwas a conceptual
structures one,that
using abductive
would reasoning.toDesign
be sufficient explainprinciples were path
the observed
used to logically infer the requisite internal structures that would be sufficient
phenomena. While such methods do not give results with the same level of quantitative formulation to explain the observed
path phenomena. While such methods do not give results with the same level of quantitative
as mathematical approaches, they do potentially allow new insights. The area under examination was
formulation as mathematical approaches, they do potentially allow new insights. The area under
the Mach–Zehnder
examination was (MZ)theinterferometer.
Mach–Zehnder (MZ) interferometer.
4. Results
4. Results
4.1. Underpinning Concepts
4.1. Underpinning Concepts
The CordusThe Cordus theory predicts
theory predicts a specific
a specific internalinternal
structurestructure for fundamental
for fundamental particles.
particles. ThisThis
comprises
comprises two reactive ends, some spatial distance apart, and connected by a fibril. The reactive ends
two reactive ends, some spatial distance apart, and connected by a fibril. The reactive ends are
are energised at a frequency, and emit discrete forces at these times [1]. Each is a type of field oscillator
energised at a frequency, and emit discrete forces at these times [1]. Each is a type of field oscillator [11].
[11]. This is a NLHV structure but with discrete fields. The structure of the photon is shown in Figure
This is a1.NLHV structure but with discrete fields. The structure of the photon is shown in Figure 1.
Characteristics of the photon are that (1) it does not release its
discrete forces, but cycles between emitting and withdrawing them
(evanescent), and (2) at any one moment both reactive ends are
energised and the discrete forces at both are in the same absolute
direction (oscillating).
Discrete force
extended in At the next frequency cycle the discrete
radial direction force is withdrawn from the fabric and
reversed. There is no enduring discrete
[r] force, so the field effect is local
(evanescent)
[t]
Motion compensates for incomplete
[a]
system of discrete forces in the three
axes.
Orientation of fibril in space
determines polarisation
Type of reactive end is oscillating: the
discrete force is extended then
withdrawn, both reactive ends are
[r] simultaneously active.
Particle interacts at two reactive ends
and through its discrete forces. Hence
this is a non-local design.
Cordus
Figure 1.Figure theorytheory
1. Cordus for the
for internal structure
the internal structureofof the photon,itsits
the photon, two
two reactive
reactive ends,ends, and
and its its discrete
discrete
field arrangements. The photon has a pump that shuttles energy outwards into
field arrangements. The photon has a pump that shuttles energy outwards into the fabric. Then the fabric. Then at the at the
next frequency cycle, it draws the energy out of that field, instantaneously transmits it across
next frequency cycle, it draws the energy out of that field, instantaneously transmits it across the fibril, the fibril,
and expels it at the opposite reactive end. Adapted from [18].
and expels it at the opposite reactive end. Adapted from [18].
The theory requires the photon to have an oscillating system of discrete fields. The discrete forces
Theare
theory requires
ejected from onethe photon
reactive endtoand
have an oscillating
(at the system
same moment) drawnofindiscrete fields.
at the other. Thenext
At the discrete
stage forces
are ejected from one reactive end and (at the same moment) drawn in at the other. At the next stage
in the frequency cycle the directions reverse. Consequently, the photon’s discrete forces are recycled.
in the frequency cycle the
This also explains whydirections reverse.
the evanescent Consequently,
field weakens the photon’s
exponentially discrete
with distance: forces
because are recycled.
the discrete
forces recruit a volume of space [12]. In contrast, massy particles such as the electron emit discreteOptics 2020, 1 246
This also explains why the evanescent field weakens exponentially with distance: because the discrete
forces recruit a volume of space [12]. In contrast, massy particles such as the electron emit discrete
forces (the direction provides the charge attribute) and release them into the external environment in
a series making up a flux tube. Hence, the electric field has an inverse radius squared relationship
because it progresses outwards as a front on the surface of an expanding sphere. The sign convention
Optics 2020, 1, FOR PEER REVIEW 4
is for outward motion of discrete forces to correspond to a negative charge, and inward motion to a
positiveforces
charge.(theConsequently,
direction provides thisthestructure also explains
charge attribute) whythem
and release the into
electric field ofenvironment
the external the photoninreverses
its sign. a series making up a flux tube. Hence, the electric field has an inverse radius squared relationship
because it progresses outwards as a front on the surface of
The explanation of the double-slit experiment is briefly summarised as follows an expanding sphere. The sign conventionfrom [1].
is for outward motion of discrete forces to correspond to a negative charge, and inward motion to a
Each reactive end of the photon particle passes cleanly through one slit. The fibril passes through the
positive charge. Consequently, this structure also explains why the electric field of the photon
materialreverses
between the two slits, but does not interact with it. The particle structure collapses when
its sign.
one of the reactive ends encounters
The explanation a medium
of the double-slit that absorbs
experiment is brieflyits discrete forces,
summarised as followsand the[1].
from whole
Eachphoton
energy then appears at this location. Consequently, whichever reactive end
reactive end of the photon particle passes cleanly through one slit. The fibril passes through the first encounters a detector
material between the two slits, but does not interact with it. The particle structure
behind the double-slit device will trigger a detection event. If there is a detector behind each slit, collapses when one
then theofvariability
the reactiveofends encountersphase
the photons’ a mediumoffsetthat absorbs
results its discrete
in the events forces,
being and
sharedthe across
whole photon
the detectors.
energy then appears at this location. Consequently, whichever reactive end first encounters a detector
Hence, a single photon appears at one or the other slit, but a stream of them looks like a wave.
behind the double-slit device will trigger a detection event. If there is a detector behind each slit, then
However, whenofonly
the variability one slitphase
the photons’ has offset
a detector, then
results in the the photon
events alwaysacross
being shared appears there. This is
the detectors.
explained as one of the two reactive ends of the particle passing through
Hence, a single photon appears at one or the other slit, but a stream of them looks like a wave.each slit, as before. Then the
whole particle collapses
However, when at only
whichever
one slit reactive end first
has a detector, thengrounds;
the photon this is always
always appearsthethere.
detector
This since
is it is
explained
first in the locus. asNo onephoton
of the two reactive travels
structure ends of the particle
beyond passing
the through
detector, eachfringes
so no slit, as before.
appearThen the screen
on the
beyond whole particle collapses at whichever reactive end first grounds; this is always the detector since it is
the detector in this case.
first in the locus. No photon structure travels beyond the detector, so no fringes appear on the screen
beyond the detector in this case.
4.2. Mach–Zehnder Interferometer
The4.2. Mach–Zehnder Interferometer
Mach–Zehnder interferometer also presents with quantum difficulties. It has two detectors at
the end of each output path (see
The Mach–Zehnder Figure 2).also
interferometer Thepresents
light beam is split into
with quantum paths It
difficulties. 1 has
andtwo
2 atdetectors
partial mirror
at the end ofat
PM1, recombines each output
partial path (see
mirror Figure
PM2, and2).then
The light beam istosplit
proceeds into paths
detectors DA1 and
and2 at partial mirror
DB.
PM1, recombines at partial mirror PM2, and then proceeds to detectors DA and DB.
Figure 2. Mach–Zehnder interferometer in default mode. The photon appears at DB.
Figure 2. Mach–Zehnder interferometer in default mode. The photon appears at DB.Optics 2020, 1 247
4.2.1. MZ with No Obstructions (Default Mode)
In the default mode, the whole beam selectively appears at one of the detectors. Conventional
optical wave theory explains this based on the different reflection and refraction delays encountered
on the two paths. The light beam experiences a phase shift of half a wavelength where it reflects off a
medium with a higher refractive index (otherwise none), and a constant phase shift k, where it refracts
through a denser medium.
The beam on path 1 to detector DB experiences k + 1⁄2 + 1⁄2 phase-shift (at a, c, and e) (see Figure 2),
whereas to reach detector DA requires an additional k (at y). Similarly, the beam on path 2 to detector
DB experiences 1⁄2 + 1⁄2 + k (at p, r, and t). As these are the same, the classical model concludes that the
two beams on 1 and 2 result in constructive interference at DB, so the whole output appears there,
providing that the optical path lengths around both sides of the interferometer are equal. Similarly,
the beam on path 2 into detector DA experiences 1⁄2 + 1⁄2 + k + k phase-shift (at p, r, t, and v), whereas the
1 beam into DA experiences k + 1⁄2 + k phase-shift (at a, c, v). As these differ by half a wavelength,
the usual explanation is that the two beams interfere destructively and no light is detected at DA.
This explanation is sufficient for continuous light beams, but not for individual photons.
4.2.2. Quantum Interpretation
This path-selective behaviour also occurs for individual photons, which might be expected to take
only one path. If one of the paths is blocked by a mirror that deflects the beam away, then the beam
still appears at DB, regardless of which path was blocked. The photon seems to “know” which path
was blocked, without actually taking it, and then takes the other. QM successfully quantifies these
outcomes [19], but leaves the physical explanation unresolved. Explanations such as self-interference,
or the existence of virtual particles, add their own problems of interpretation.
4.3. Explanation of MZ Interferometer Behaviour with the Cordus Theory
Considering the Cordus particle with its two ends, it might naively be thought that each reactive
end (RE) takes a different path, with the phase difference through the glass at y causing the reactive
end to be delayed and, hence, not appearing at detector DA. However, this is unsatisfactory because a
decision tree of the path options shows that 1⁄4 of photons should still appear at detector DA even if DA
is precisely located relative to DB. The solution involves reconceptualising what happens at the partial
mirrors. Specifically, the following mechanisms are proposed (these are lemmas):
1. In a full-reflection, i.e., off a mirror, both reactive ends of the photon particle, which are separated
by the span, independently reflect off the mirror.
2. Reflection does not collapse the particle, i.e., the photon is not absorbed, but rather continues on
a locus.
3. When encountering a partially reflective surface, e.g., a beam-splitter or partially silvered mirror,
the outcome depends on the state (energised vs. dormant) of the reactive end at the time of
contact. Specifically:
3.1 A reactive end will reflect off a mirror only if it is predominately in one state, nominally
assumed to be the energised state, when it encounters the reflective layer.
3.2 A dormant reactive end passes some way into a reflective layer without reacting. Only if it
re-energises within the layer will it be reflected.
3.3 If the reflective layer is thin enough, a dormant reactive end may re-energise on the other
side of layer, in which case it is not reflected. Hence, the reactive end tunnels through the
layer, and re-energises beyond it.
3.4 The thickness of the layer is therefore predicted to be important, relative to the displacement
in space that the reactive end can make. The latter is determined by the velocity and
frequency of the particle.Optics 2020, 1 248
Optics 2020, 1, FOR PEER REVIEW 6
4. The orientation of the particle, i.e., polarisation of a photon or spin of an electron, as it strikes the
4 beam-splitter
The is of
orientation important in the
the particle, outcome.
i.e., polarisation of a photon or spin of an electron, as it strikes
the beam-splitter is important in the outcome.
4.1 If the reactive ends strike with suitable timing such that each, in turn, is energised as it
4.1 Ifengages
the reactive ends
with the strikethen
surface, withthe
suitable
whole timing
particlesuch that
may be each, inLikewise,
reflected. turn, is energised as it
if both reactive
engages with the surface, then the whole particle may be reflected. Likewise, if
ends are dormant at their respective engagements, then the whole particle is transmitted. both reactive
4.2 It is are
ends dormant
possible that at their
only onerespective engagements,
reactive end is reflectedthen
andthe
thewhole particle is transmitted.
other transmitted. In this case,
4.2 Itthe
is possible that only one reactive end is
beam-splitter changes the span of the photon.reflected and the other transmitted. In this case,
the beam-splitter changes the span of the photon.
5. The span of a photon is not determined by its frequency.
5 The span of a photon is not determined by its frequency.
5.1 The photon span is initially determined at its original emission per [12], but is able to be
5.1 The photon span is initially determined at its original emission per [12], but is able to be
changed subsequently. The reactive ends follow the surfaces of any wave guides that might
changed subsequently. The reactive ends follow the surfaces of any wave guides that might
be encountered, and the span may change as a result. This has no energy implications for
be encountered, and the span may change as a result. This has no energy implications for
the photon.
the photon.
5.2 In contrast to massy particles, e.g., electrons, the span is inversely related to the frequency
5.2 In contrast to massy particles, e.g., electrons, the span is inversely related to the frequency
and, hence, to the energy.
and, hence, to the energy.
These principles
These principles are
are summarised
summarised in
in Figure
Figure 3.
3.
Figure 3. A beam-splitter reflects only the energised reactive end. The dormant
dormant reactive end passes
through. The
The diagram
diagram shows
shows aa p-polarised
p-polarised photon,
photon, but
but the
the principles
principles generalise
generalise to
to other
other forms
forms of
polarisation. The
The key
key determinant
determinant of
of the
the path
path is
is the
the state (energised/dormant)
(energised/dormant) of
of the pair of reactive
ends at contact with the mirror.
The implication
implication is is that
that a reactive end reflects if it is in a suitably energised state at the point of
Otherwise itit progresses
contact. Otherwise progresses deeper
deeper into
into the
the material,
material, andand may
may have
have a further opportunity
opportunity to
energise and
andbebereflected. If itIfmanages
reflected. to pass
it manages to entirely throughthrough
pass entirely the reflective layer without
the reflective energising,
layer without
then it has avoided reflection altogether. This outcome requires a reflective layer
energising, then it has avoided reflection altogether. This outcome requires a reflective layer thin enough relative
thin
to the distance
enough relativethe RE can
to the travelthe
distance before
RE canre-energising,
travel beforei.e., relative to the
re-energising, wavelength.
i.e., relative to the wavelength.
Hence, for a photon striking the partial mirror, there are three possible outcomes: both reactive
ends reflect; neither reflect (both transmit through); or one reactive end reflects and the other
transmits. The latter sends the reactive ends on non-parallel paths and changes the span of the
photon.Optics 2020, 1 249
Hence, for a photon striking the partial mirror, there are three possible outcomes: both reactive
ends
Opticsreflect; neither
2020, 1, FOR PEERreflect
REVIEW (both transmit through); or one reactive end reflects and the other transmits.7
The latter sends the reactive ends on non-parallel paths and changes the span of the photon.
These
Theseoutcomes
outcomesdepend
depend onon
thethe
orientation (polarisation)
orientation of theof
(polarisation) particle, the precise
the particle, the phase
precise location
phase
of the energised reactive end when it makes contact, and the frequency relative
location of the energised reactive end when it makes contact, and the frequency relative to the to the thickness of
the mirror.of the mirror.
thickness
The
The lemmas
lemmas also
also explain
explain the
the observed
observed variable
variable output
output of the beam-splitter,
beam-splitter, whereby
whereby two two beams
beams
generally
generally emerge.
emerge. This may be explained as the variable variable orientations
orientations (polarisations)
(polarisations) of the the input
input
photons
photons resulting
resultingin in all
all three
threeoutcomes
outcomesoccurring.
occurring. Furthermore,
Furthermore, itit is
is observed
observed that
that ifif the
the polarisation
polarisation
of
of the
the input
input beam
beam isis changed
changed thenthen the
thebeam
beamsplitter
splitterwill
willfavour
favouroneoneoutput.
output. This,
This, too,
too, is
is consistent
consistent
with
with the
the above
aboveCordus
Cordusexplanation.
explanation.
4.3.1.
4.3.1. Explanation
Explanation of
of MZ
MZ Interferometer
Interferometer in
in Default
Default Mode
Mode
Having
Having established
established the
the engagement
engagement mechanisms
mechanisms expressed
expressed inin the
the lemmas,
lemmas, thethe explanation
explanation ofof
the MZ device may now be continued. We consider a single photon, but the principles
the MZ device may now be continued. We consider a single photon, but the principles generalise to generalise
to a beam
a beam of of many.
many. TheThe photon
photon reaches
reaches partial
partial mirror
mirror PM1PM1 (see(see Figure
Figure 4). energised
4). The The energised reactive
reactive ends
ends reflect
reflect off mirror,
off the the mirror,
andand
thethe dormant
dormant REs
REs transmitthrough.
transmit through.Depending
Dependingon on the
the polarisation
polarisation and
and
frequency
frequency states of the photons, some whole photons go down path 1, some down 2, and some are
states of the photons, some whole photons go down path 1, some down 2, and some are
split
split to
to go
go down
down both.
both.
Figure 4.
Figure 4. Photon
Photon particle
particle interaction
interaction with
with the
the first
first partial
partial mirror
mirror of
of the
the Mach–Zehnder interferometer.
Mach–Zehnder interferometer.
Thewhole
The wholephotons
photonspose posenono particular
particular problem,
problem, butbut a split
a split photon
photon needsneeds explanation.
explanation. Reactive
Reactive end
end a1 reflects off the surface and continues on path 2 (pqrst). The dormant
a1 reflects off the surface and continues on path 2 (pqrst). The dormant a2 reactive end passes through a2 reactive end passes
through
the mirrorthe mirrorre-energises
surface, surface, re-energises beyond
beyond it (e.g., in theit transparent
(e.g., in thebacking
transparent backing
material), andmaterial),
continuesandon
continues on path 1 (abcd). The order is unimportant; it is not necessary
path 1 (abcd). The order is unimportant; it is not necessary that the energised reactive end reaches that the energised reactive
endsurface
the reachesbeforethe surface before reactive
the dormant the dormant
end. reactive end. end
The reactive The that
reactive
was end that was
energised energised
at the at the
mirror (a1 in
mirror
this case)(a1 in this reflected
is always case) is (takes
always reflected
path 2). This(takes path 2).
is important This
in the is important
following in the Assuming
explanation. following
explanation.
equal opticalAssuming
path length equal
alongoptical
1 andpath lengthisalong
2, which 1 andsince
the case 2, which is the caseis
the apparatus since theto
tuned apparatus
achieve
is tuned
this, thento achieve
both this,ends
reactive thencome
both together
reactive ends
againcome together
at partial again
mirror PM2, at partial
havingmirror PM2, several
undergone having
undergonereversals.
frequency several frequency reversals.
The explanation assumes
The assumes that thatthe
thepath
pathlength
lengthisissuchsuchthat the
that reactive
the reactive ends at PM2
ends at PM2areare
all in
allthe
in
opposite
the opposite statestate
to PM1,
to PM1, i.e., i.e.,
the path lengths
the path are not
lengths are only equal,
not only but abut
equal, whole eveneven
a whole multiple of half-
multiple of
wavelengths. The The
half-wavelengths. particles thatthat
particles have travelled
have whole
travelled whole downdown path
path1 1oror2 2now
nowdivert
divertto
to detector
detector DB.
Theexplanation
The explanationfor forthethesplit
split particles
particles follows:
follows: when
when reactive
reactive endend a1 reaches
a1 reaches the mirror
the mirror surface
surface of PM2 of
itPM2 it is in
is now nowtheindormant
the dormant state,state, and therefore
and therefore passespasses
through through to detector
to detector DB. By DB.contrast,
By contrast, reactive
reactive end
end a2, which was dormant at PM1, is now energised at PM2, and reflects, taking it also to detector
DB (see Figure 5).Optics 2020, 1 250
a2, which was dormant at PM1, is now energised at PM2, and reflects, taking it also to detector DB
(see Figure 5).
Optics 2020, 1, FOR PEER REVIEW 8
Figure5.5.Photon
Figure Photonbehaviour
behaviouratatsecond
secondpartial
partialmirror
mirrorofofthe
theMach–Zehnder
Mach–Zehnderinterferometer.
interferometer.
Consequently,the
Consequently, the photon
photon always
always appears
appearsatatdetector
detectorDB, DB,regardless
regardless of of
which
whichpath
pathit took. The
it took.
arrangement
The arrangement of the
ofpartial mirrors
the partial and the
mirrors andspace
the between achieveachieve
space between this by the
thissecond
by themirror
secondreversing
mirror
the operation
reversing of the first.
the operation Thisfirst.
of the operation occurs whether
This operation the reactive
occurs whether the ends of aends
reactive photon
of atake
photon the same
take
path
the (whole
same pathphoton) or different
(whole photon) paths (split
or different pathsphoton). The effect
(split photon). Theholds
effect for a single
holds photon
for a single and many
photon and
individual
many photons;
individual hence,hence,
photons; the behaviour may bemay
the behaviour observed at macroscopic
be observed scales with
at macroscopic beams
scales with or light.
beams
The apparent intelligence in the system is not because the photons know which path to take, but
or light.
ratherThebecause
apparent theintelligence
MZ interferometer is a finely-tuned
in the system is not because photon-sorting
the photonsdeviceknowthat whichauto-corrects
path to take, for
randomness
but in thethe
rather because frequency phase.
MZ interferometer is a finely-tuned photon-sorting device that auto-corrects for
The layout
randomness in theoffrequency
an interferometer
phase. is usually taken for granted. However, such devices only work
by design or tuning.
The layout The layout of the
of an interferometer MZ or taken
is usually any other interferometer
for granted. However, is decided beforehand
such devices only work and bythe
apparatus is tuned by moving the components relative to each other until
design or tuning. The layout of the MZ or any other interferometer is decided beforehand and the the expected functionality
is obtained.
apparatus Consequently,
is tuned by moving the layout is actually
the components relativea toset
eachof other
additional covert
until the variables
expected which the
functionality is
observer Consequently,
obtained. (even if unknowingly)
the layout imposes on the
is actually a setexperiment.
of additional This imposition
covert variablesenables
whichand limits the
the observer
waysifthe
(even apparatus can
unknowingly) behave.on
imposes The
thepartial mirrorsThis
experiment. provide the ability
imposition to send
enables andthe reactive
limits the waysends the
of a
photon down
apparatus differentThe
can behave. paths, but the
partial ability
mirrors to recombine
provide them
the ability to at onethe
send detector
reactiverather
endsthan
of athe other
photon
is a consequence
down different paths,of how butthe
theinterferometer is designed
ability to recombine themand the detector
at one precisionrather
to whichthanthe
thepath
otherlengths
is a
are tuned. The
consequence of detector
how the at which the photon
interferometer appearsand
is designed canthebe precision
controlledtobywhich
adjusting the path
the path lengths.
lengths are
tuned. The detector at which the photon appears can be controlled by adjusting the path lengths.
4.3.2. MZ Interferometer in Open-Path Mode
4.3.2. MZ Interferometer in Open-Path Mode
Conventionally, the wave-particle dilemma occurs when one of the paths is blocked, since it
Conventionally,
suggests the wave-particle
the weird solution that the photon dilemma
“knew” occurs
which when
pathone
wasofblocked
the paths is blocked,
without actually since
takingit
suggests the weird solution that the photon “knew” which path was blocked
it. A mirror may be inserted at either D or S to deflect the beam away, but the photon nonetheless without actually taking it.
Aappears
mirror may be inserted
at detector DBat (see
eitherFigure
D or S 6),to deflect
despite thethe
beam away, but
apparent the photon
mutual nonetheless
exclusivity of theseappearstwo
atexperiments.
detector DB (see Figure 6), despite the apparent mutual exclusivity of these two experiments.Optics 2020, 1 251
Optics 2020, 1, FOR PEER REVIEW 9
Figure
Figure6.
6. Inclusion
Inclusionof
ofan
anextra
extramirror
mirrorat
atD
Dstill
stillresults
resultsin
in photons
photons arriving
arriving at
at detector
detector DB.
DB.
From the
From the Cordus
Cordus theory
theory the
the explanation
explanation is is as
as follows:
follows: the
the layout
layout of of the
the interferometer
interferometer ensures
ensures
that those reactive ends that are not impeded will be forced by the partial mirrors to converge atatDB.
that those reactive ends that are not impeded will be forced by the partial mirrors to converge DB.
Regardless of
Regardless of which
which path,
path, 11 or
or2,
2,isisopen-circuited,
open-circuited,the theremaining
remaining whole
whole photons
photons andand the
thesplit
splitphotons
photons
(providing they are
(providing are not
notabsorbed
absorbedfirst firstatatg)g)will
willalways
always appear
appearat DB.
at DB.Note thatthat
Note the the
theory provides
theory that
provides
the whole
that energy
the whole of a of
energy photon collapses
a photon collapsesat the location
at the where
location wherethe the
firstfirst
of its
of reactives is grounded
its reactives [1].
is grounded
TheThe
[1]. detectors are are
detectors devices specifically
devices specificallydesigned
designedto perform this this
to perform collapse.
collapse.
4.3.3. MZ
4.3.3. MZInterferometer
Interferometer in
in Sample
Sample Mode
Mode
The MZ
The MZdevice
devicemaymaybebeusedusedtoto measure
measure thethe refractivity
refractivity ks aoftransparent
ks of a transparent samplesample placed
placed in
in one
one of the legs, say S. The observed reality when using a beam of photons is
of the legs, say S. The observed reality when using a beam of photons is that a proportion of the beamthat a proportion of the
beamappears
now now appears at detector
at detector DA. DA.The The
wave wave
theorytheory adequately
adequately explains
explains this
this basedononphase
based phaseshift
shiftand
and
constructive (destructive)
constructive (destructive) interference,
interference, but but cannot
cannot explain
explain why
why the
the effect
effect persists
persists forfor single
single photons.
photons.
The Cordus explanation is that the sample introduces a small time delay
The Cordus explanation is that the sample introduces a small time delay to the (say) a1 reactive to the (say) a1 reactive
end of the split photon, so it arrives slightly late at partial mirror PM2. If sufficiently
end of the split photon, so it arrives slightly late at partial mirror PM2. If sufficiently late, then late, then a2a2
reaches the
reaches the mirror
mirror inin an
an energised
energised state
state (it(it usually
usually would
would bebe dormant
dormant at at this
this point),
point), andand therefore
therefore
reflects and passes to detector DA. If a2 is only partially energised when it
reflects and passes to detector DA. If a2 is only partially energised when it reaches the mirror, reaches the mirror, then its
then
destination
its destination is less certain;
is less a single
certain; photon
a single will go
photon willtogoonetoorone
theor
other
the detector depending
other detector on its precise
depending on its
state at the time. The proportioning is proposed to occur when a beam of photons
precise state at the time. The proportioning is proposed to occur when a beam of photons is involved, is involved, as the
as the random variabilities will place them each in slightly different states, and, hence, cause them to
head to different detectors.Optics 2020, 1 252
random variabilities will place them each in slightly different states, and, hence, cause them to head to
different detectors.
If path 1 or 2 in the MZ device is totally blocked by an opaque barrier (unlike the mirror mode),
then the whole particles in that leg ground there, as do the split particles. However, the whole particles
in the remaining leg continue to DB as before.
4.4. Explanation of Tunnelling
The partial mirror may be considered to operate on tunnelling effects, per lemma 3.3. The same
principles also explain other tunnelling phenomena involving a barrier. The “barrier” could be a
reflective surface, layers within prisms, or a non-conductive gap for electrons, e.g., Josephson junction.
The tunnelling effect is not explained by classical mechanics, but is by quantum mechanics.
The typical QM explanation follows an energy line of thinking: the barrier requires a higher energy
to overcome; the zero-dimensional particle is occasionally able to borrow energy from the external
environment; it uses this to traverse the gap; the energy is then returned to the environment.
The Heisenberg uncertainty principle provides the mechanism for the underlying indeterminism of
energy. For QM, the randomness of tunnelling arises due to not all particles being able to borrow the
necessary energy.
In contrast, the proposed Cordus mechanism shows that the reactive end of a particle does not
react to the barrier when in the dormant state. If the dormant reactive end can completely traverse the
barrier before re-energising, then it passes through the barrier. The other reactive end may likewise
have an opportunity to do so; hence, the whole particle may jump the barrier. The thickness of the
barrier is a known detriment to tunnelling, and this is consistent with the Cordus explanation.
The Cordus concept of the fibril providing instantaneous co-ordination between reactive ends is
also consistent with the observation that some tunnelling effects can be superluminal and non-local [20].
For the Cordus theory, the randomness of tunnelling arises due to the variability of the particle’s
orientation and phase when it meets the barrier and is not primarily an energy borrowing phenomenon.
We thus make the falsifiable prediction that with suitable control of frequency, orientation, and phase,
it should be possible to get all incident particles to cross the barrier.
5. Discussion
We have shown that it is possible to give an explanation for the path dilemmas in the MZ
interferometer, in its various modes, for single photons and beams. The results show that it is possible
to conceive of explanations based on physical realism. This does not require virtual particles, parallel
worlds, pilot waves, or intelligent photons. Nonetheless, what it does require is physical structures at
the sub-particle level, i.e., a non-local, hidden-variable solution. Importantly, while the solution requires
some premises, these are not unreasonable and are not precluded by empiricism or other physics.
Dirac was of the view that photons only interfered within themselves, not with other photons [3].
The present theory is consistent therewith. It proposes a type of dipole structure for the photon,
with co-ordination occurring between the two ends, and the ability of the two ends to take different
optical paths. The theory is also accepting of quantum field theory with its oscillators and fields,
but diverges by proposing a specific internal structure to the particle and a physical mechanism for
the tunnelling effect. Hence, while the NLHV perspective might seem foreign and incompatible from a
quantum theory perspective, it appears there may be significant areas of agreement.
The contribution of the work is, therefore, its explanation of interferometer and tunnelling
behaviour in terms of physical realism and NLHV theory.
5.1. Implications
The work demonstrates a new way to conceptualise fundamental physics other than via the
stochastic properties of 0-D points. Allowing particles to have internal structure yields explanations
of interferometer behaviour and tunnelling. The wider implication is that the stochastic nature ofOptics 2020, 1 253
quantum mechanics is interpreted as a simplification of a deeper NLHV mechanics. The Cordus theory,
therefore, provides a means to conceptually reconnect the mathematics of quantum theory to physical
realism. Given that the Cordus theory spans diverse areas of physics (optics, particles, cosmology),
which other theories struggle to achieve, this work suggests that the NLHV sector is not as barren as
it seems.
5.2. Limitations
The major limitation of the theory is that its explanations are conceptual and it does not yet have
a mathematical formalism to represent the particle concept. This makes it difficult to represent the
concepts, e.g., its explanations for the MZ interferometer behaviour, to the same level of quantitative
detail that is available to quantum mechanics.
5.3. Future Research Opportunities
There is an opportunity for future research to develop a mathematical representation of the
particle behaviour. This is a call for a novel mathematical approach, since there are multiple physical
structures at the sub-particle level that need to be represented. There are also several empirical research
opportunities. One could be to test the tunnelling mechanism proposed here for the partial mirror
(see also the falsifiable prediction above). Another could be to devise other ways of disrupting the
MZ interferometer to test the proposal that the reactive ends of the photon occasionally go down
different legs, i.e., the photon span is stretched to macroscopic dimensions. The Cordus theory is a
proto-physics or candidate theory of new physics, and consequently there are also many possibilities
for future research of a conceptual nature.
6. Conclusions
One of the central quantum dilemmas of the wave-particle duality is the ambiguity of where the
photon is going and which path it will take. Existing approaches either reconfigure the photon as a
wave or treat the problem as simply probabilistic. The present work suggests that the locus of the
photon is determined by the orientation and frequency state of its reactive ends when they meet a
partial mirror. Furthermore, it is proposed that each of the two reactive ends of the Cordus particle
may take a different locus. Hence, the theory is able to explain the behaviour of the Mach–Zehnder
interferometer in its three modes: default-, open path-, and sampling-mode.
The Cordus theory provides a conceptual framework for how physical theory may be extended
to levels more fundamental than currently reached by wave theory or quantum theory. This has the
potential to provide a new understanding of photon behaviour in unusual situations. In summary,
the present results show that the Mach–Zehnder interferometer is an unexpectedly finely-tuned
passive photon-sorting device that auto-corrects for randomness in the frequency phase. It behaves
somewhat like a macroscopic optical meta-material.
Author Contributions: The authors of [21] contributed to the development of the idea for the Cordus particle and
the explanation for wave particle duality [1]. D.J.P. developed the explanations for the photon path dilemmas for
the current paper. The author has read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The author declares that there is no financial conflict of interest regarding this work.
The research was conducted without personal financial benefit from a third party funding body, nor did any such
body influence the execution of the work.
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